Per the source, the Gunners are satisfied with the offer and the deal will be confirmed over the next few days if personal terms are agreed between Galatasaray and the French international full-back.
There was however, no mention of the €3 million release clause option Galatasaray want to include in the contract according to reports from Turkey.
The reports from France follow Galatasaray sporting director Levent Nazifoglu confirming the transfer link.
“Mathieu Debuchy was offered to Galatasaray through his agent on a loan deal,” Nazifoglu was quoted as saying by Turkish-football.com.
The Lions are keen on strengthening their full-back position over the summer as head coach Jan Riekerink has not been impressed with Linnes and Sabri.
Debuchy has two goals in 27 caps for France since making his international debut back in 2011 but was ruled out of Euro 2016 with a hamstring injury.
The 31-year-old joined Arsenal from Newcastle United back in 2014 for £12.75 million but has made just 22 appearances in all competitions since his arrival.